This document discusses laser beam characteristics including: 1. Lasers produce monochromatic, coherent beams with high directionality and low divergence. 2. Coherence refers to the correlation between the phases of waves and is measured both temporally and spatially. 3. An example calculates the coherence length and time for a laser beam filtered to have a bandwidth of 10 nm and wavelength of 532 nm.

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6/14/20151
412 PHYS
Lasers and their Applications
Department of Physics
Faculty of Science
Jazan University
KSA
Lecture-5
Laser Beam characteristics
• Monochromaticity
• High directionality
• Coherence
• Low divergence
• Brightness or radiance
• Focusing characteristics
• Pulsed and CW operation
• Available high power operations
• Tunability
• Ultra-short duration pulse
Laser Beam Characteristics

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0 /D   
• Monochromaticity
0  Monochromaticity
0 Central
frequency
Single wavelength
Coherence is a measure of the correlation between the phases measured at
different (temporal and spatial) points on a wave
Coherence theory is a study of the correlation properties of random light
which is also known as the statistical optics
Coherence

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Monochromatic & Coherence:
Incoherent beam
Time
Space
Perfect Coherent
2
/CL c



  

Coherence Length
1/c  
Coherence time
Note that
C cL c 

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Example:
If a spectral filter with a bandwidth of 10 nm is used to obtain a
monochromatic light of wavelength of 532nm from a white light source.
Calculate the length ad time of coherence
2 9 2
9
(532 10 )
28.30
10 10
cl m






  
 
Solution:
6
14
8
1 28.30 10
9.4 10 94
3 10
c
c
l
s fs
c




     
 
Beam divergence
Laser beam is highly directional, which implies laser light is of very small
divergence. This is a direct consequence of the fact that laser beam comes
from the resonant cavity, and only waves propagating along the optical axis
can be sustained in the cavity. The directionality is described by the light
beam divergence angle. Please try the figure below to see the relationship
between divergence and optical systems.
/ d   Numerical factor
 1.22  For uniform optical beams
 2/  For Gaussian beams
For perfect spatial coherent
light, a beam of aperture
diameter d will have unavoidable
divergence because of
diffraction. From diffraction
theory, the divergence angle

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Focusing of laser radiation
To determine the value of the available power density from a laser
beam we need to consider the laser spot size at which the beam is
focused
The spot size is a diffraction –limited parameter, i.e.,
It has a maximum value that can not be exceeded
sr f 
The divergence angle for a diffraction-limited
beam is given by: / D 
D: is the limiting aperture /sr f D F  
F: is known as the F-number of the lens which can be
expressed in terms of the lens focal length as
/F f D
For F=1, ( )sr 
The available power density is given by
2
.4 /D totP P f

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Beam expander for low divergence beam
ffii dd  
In terms of focal length
12i fd f f
Example
A He-Ne Laser with a wavelength of 633nm. Its beam radius measured at 2
1/ e
From maximum intensity is 50 m, what will be its value at waist?
Solution
0/ ( )d w  The divergence angle is given by
sin( / 2) tan( / 2) / 2  
3 9
4 4
0
0
50 10 633 10
/ 2 2.5 10 5 10
200 3.14
0.04
d
w
w mm
 
 
  
      
 

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Example
A beam from a He-Ne laser with a diameter of 1.5 mm and a divergence of
1mrad. If a beam expander system consists of two convex lenses of focal
lengths of 1 cm and 5 cm is used. Find the diameter and divergence of the
resulted beam
Solution
31 1 2 2
2 1
2 2 1 1
1.5 5 7.5 10
f d f
d d mm
f d f



       
3
2 1 21/ 1 10 / 5 0.167f f mrad  
   
Depth of focus
This a very important property of the laser beam
It is defined as the distance from waist point at which the intensity
decreases from its maximum by 5% at both sides
It is usually defined as the double of the Rayleigh range
2
0
0
2
2f
w
D z


 
And in terms of the lens F-number
2
2 s
f
r
D F   
2w0
DOF
rs
f

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Example:
Find the intensity and depth of focus for an Ar laser beam with a
power of 1W and divergence of 0.5mrad if the beam is collimated
by a convex lend of a focal length of 5 cm?
solution
3 3
5 (0.5 10 ) 2.5 10s sr f r cm  
      
2 3 2 6 2
(2.5 10 ) 20 10sA r cm   
    
Spot size
Spot area
4 2 8 2
6
1
5 10 [ / ] 5 10 [ / ]
20 10
P
I W cm W m
A 
     
The intensity
2 3 2 2
7
(2.5 10 )
0.099 1
633 10
s
f
r cm
D cm mm
cm



   

The depth of focus
The brightness of a light source is defined as the power emitted per unit
surface area per unit solid angle.
Brightness
cos( )
P
B
ds d


Spectral brightness
cos( )
P
B
ds d

 

 

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Example
Compare an ordinary light source of a wavelength of 546nm and
brightness 2
95( / )W cm sr
With a diffraction – limited Argon laser beam of a wavelength of 514.5nm
and a power of 1W
Solution 1.2 /d D   For a diffraction-limited beam
2 2 2
4
( / 2) (1.2 )
P P P
B
dS d D   
  

For Ar laser 12 2
9 2
4(1)
1.531 10 / ( )
(1.2 3.14 514.5 10 )
ArB W m sr
  
  
8
61.531 10
1.611 10
95
Ratio

 